Question

Find \(\int_0^{\frac{π}{2}} \,5 \,sin⁡x \,dx\).

(a) -5

(b) 9

(c) 5

(d) -9

I have been asked this question during an online interview.

The above asked question is from Fundamental Theorem of Calculus-1 topic in chapter Integrals of Mathematics – Class 12

Answer 1

The correct answer is (c) 5

The best explanation: Let \(I=\int_0^{\frac{π}{2}} \,5 \,sin⁡x \,dx\)

F(x)=\(\int5 \,sin⁡x \,dx=-5 \,cos⁡x\)

Applying the limits by using the fundamental theorem of calculus, we get

I=F(\(\frac{π}{2}\))-F(0)

∴\(\int_0^{\frac{π}{2}} \,5 \,sin⁡x \,dx=-5[cos⁡\frac{π}{2}-cos⁡0]\)

=-5[0-1]=5